Question

modeling real life the table shows the research activities of two students at an observatory. how much does a student pay to use the telescope for one hour? telescope use supercomputer use total cost student 1 5 hours 3 hours $70.50 student 2 6 hours 2 hours $67.00 a student pays $\square$ to use the telescope for one hour. how much does a student pay to use the supercomputer for one hour? a student pays $\square$ to use the supercomputer for one hour.

Explanation:

Step1: Define variables

Let $x$ = cost/hour for telescope, $y$ = cost/hour for supercomputer.

Step2: Set up equations

For Student 1: $5x + 3y = 70.50$
For Student 2: $6x + 2y = 67.00$

Step3: Simplify Student 2's equation

Divide by 2: $3x + y = 33.50$, so $y = 33.50 - 3x$

Step4: Substitute $y$ into Student 1's equation

$5x + 3(33.50 - 3x) = 70.50$
$5x + 100.50 - 9x = 70.50$
$-4x = 70.50 - 100.50$
$-4x = -30$
$x = \frac{-30}{-4} = 7.50$

Step5: Solve for $y$

$y = 33.50 - 3(7.50) = 33.50 - 22.50 = 11.00$

Answer:

A student pays $\$7.50$ to use the telescope for one hour.
A student pays $\$11.00$ to use the supercomputer for one hour.